The US dollar literally is constructed as needed. It's pretty darn close to free thanks to electronic banking.
However, like all magic, using it has severe (and generally predictable) consequences.
Unlike fictional magic, the consequences take 4 years to kick in like clockwork. That, and the US's two term limit meant that presidents get to print money without political consequence. Worst case, they lose the midterms, then run again while blaming the next guy for the problem they created.
Presidents don't print money. Congress approves stimuli in the form of spending. Spending is always inflationary in nature because it injects money into the economy.
The Federal Reserve, nearly completely independent (for better or worse) from the Executive and Legislative branches, prints money in the form of quantitative easing and controls other levers through lending and interest rate strategies.
It's free if you spend it on a durable asset that is as or more valuable than the cash was, which can often be true of infrastructure. Your balance sheet goes up not down after the spend then.
There are vanishingly few examples of infrastructure spending that don't turn into massive, wasteful boondoggles; perhaps the Interstate Highway system.
The national railroad system a century prior and even the Internet were nearly entirely built with private funds.
The interstate highway system is arguably a massively wasteful boondoggle - it subsidises trucks at the cost of the far more efficient and less-polluting rail.
I wouldn't say vanishingly few. Seems like the vast majority of infrastructure built before some certain point in the mid-to-late 20th century was cheap and easily worth it (and we built a TON of it all the time) and it's only since then there's been increasing issues. I don't think it's about infrastructure, there's something else causing the cost overruns and we should figure out what it is.
Railroads got massive subsidies in at least two forms: huge land grants, and the power of the U.S. Army to wage war on the native peoples who otherwise would have stood in their way.
The land grant thing is sort of weird though. Hard to think of it as that big of a subsidy when the land was so so low in value prior to the railroad and the railroad's construction is what made the adjoining land so valuable. I wouldn't call it a subsidy at all -- but rather an investment that turned nearly worthless land into much more valuable land and attracted much more investment dwarfing the original "subsidy"
It's amusing and a bit scary that someone thinks the federal budget is essentially free money, constructed as needed.